this one is a bit different, here we have a first order inhomogeneous differential equation. now that may sound bad, but in differential equations that's just another way of saying "one of the easiest kinds of problems you will get." now this particular one is kind of complicated, and you'll see why, but it could be worst.

first we need to find an integrating factor. experience will tell you in this case e^-x, so we will multiply through by that. If you have problems with finding integrating factors, tell me. however, my recommendation would be to read your text book, it's kind of complicated to explain if you are new to the concept.

=> (e^-x)y' - (e^-x)y = (e^-x)x^2
but now we realize, that on the right, we have what we would have gotten if we had differentiated (e^-x)y implicitly using the chain rule, so we have

d/dx[(e^-x)y] = (e^-x)x^2 ........now we integrate both sides
=> (e^-x)y = int{(e^-x)x^2}dx .....we have to use integration by parts for this